Quasinormal modes of a Schwarzschild black hole within the Bondi-Sachs framework
arXiv:2407.06636 · doi:10.1103/PhysRevD.111.044002
Abstract
Studies of quasinormal modes (QNMs) of black holes have a long and well established history. Predominantly, much research in this area has customarily focused on the equations given by Regge, Wheeler and Zerilli. In this work we study linearized perturbations of a Schwarzschild black hole using the Characteristic formulation of numerical relativity, with an emphasis on the computation of QNMs. Within this formalism, the master equation describing gravitational perturbations is known to satisfy a fourth order differential equation. We analyse the singular points of this master equation, and obtain series solutions whose coefficients are given by three term recurrence relations, from which Leaver's continued fraction method can be applied. Using this technique, we recover the standard Schwarzschild quasinormal modes. In addition, we find that imposing purely outgoing boundary conditions, a natural feature of the Bondi-Sachs framework, leads to the recovery of the algebraically special mode.
arXiv comment12 pages, 2 figures, published in PRD
References in corpus (26)
- Quasinormal modes of black holes and black branes
- Quasi-Normal Modes of Stars and Black Holes
- Quasinormal modes of black holes: from astrophysics to string theory
- Asymptotic iteration method for eigenvalue problems
- Merger of binary neutron stars to a black hole: Disk mass, short gamma-ray bursts, and quasinormal mode ringing
- High-powered Gravitational News
- Bondi-Sachs Formalism
- Extraction of Gravitational Waves in Numerical Relativity
- Head-on collision of two black holes: comparison of different approaches
- Black hole quasinormal modes using the asymptotic iteration method
- The eth formalism in numerical relativity
- Mode coupling in the nonlinear response of black holes
- On an Expansion Method for Black Hole Quasinormal Modes and Regge Poles
- Analytic treatment of black-hole gravitational waves at the algebraically special frequency
- Characteristic Evolution and Matching
- Linearized solutions of the Einstein equations within a Bondi-Sachs framework, and implications for boundary conditions in numerical simulations
- Scalar field induced oscillations of neutron stars and gravitational collapse
- Numerical validation of the Kerr metric in Bondi-Sachs form
- Light Cone Structure near Null Infinity of the Kerr Metric
- Quasi-Normal Modes of a Schwarzschild White Hole
- Characteristic Formulation for Metric Gravity
- A characteristic approach to the quasi-normal mode problem
- Observational cosmology using characteristic numerical relativity: Characteristic formalism on null geodesics
- Simple, explicitly time-dependent and regular solutions of the linearized vacuum Einstein equations on a null cone
- Slowly rotating Kerr metric derived from the Einstein equations in affine-null coordinates
- Master equation solutions in the linear regime of characteristic formulation of general relativity